High Angular Resolution Electron Backscatter Diffraction Research Articles

The impact of water on slip system activity in olivine and the formation of bimodal crystallographic preferred orientations

Crystallographic preferred orientations (CPOs) in olivine are widely used to infer the mechanisms, conditions, and kinematics of deformation of mantle rocks. Recent experiments on water-saturated olivine were the first to produce a complex CPO characterised by bimodal orientation distributions of both [100] and [001] axes and inferred to form by combined activity of (001)[100], (100)[001], and (010)[100] slip. This result potentially provides a new microstructural indicator of deformation in the presence of elevated concentrations of intracrystalline hydrous point defects and has implications for the interpretation of seismic anisotropy. Here, we document a previously unexplained natural example of this CPO type in a xenolith from Lesotho and demonstrate that it too may be explained by elevated concentrations of hydrous point defects. We test and confirm the hypothesis that combined (001)[100], (100)[001], and (010)[100] slip were responsible for formation of this CPO by (1) using high-angular resolution electron backscatter diffraction to precisely characterise the dislocation types present in both the experimental and natural samples and (2) employing visco-plastic self-consistent simulations of CPO evolution to assess the ability of these slip systems to generate the observed CPO. Finally, we utilise calculations based on effective-medium theory to predict the anisotropy of seismic wave velocities arising from the CPO of the xenolith. Maxima in S-wave velocities and anisotropy are parallel to both the shear direction and shear plane normal, whereas maxima in P-wave velocities are oblique to both, adding complexity to interpretation of deformation kinematics from seismic anisotropy.

New levels of high angular resolution EBSD performance via inverse compositional Gauss–Newton based digital image correlation

Conventional high angular resolution electron backscatter diffraction (HREBSD) uses cross-correlation to track features between diffraction patterns, which are then related to the relative elastic strain and misorientation between the diffracting volumes of material. This paper adapts inverse compositional Gauss Newton (ICGN) digital image correlation (DIC) to be compatible with HREBSD. ICGN-based works by efficiently tracking not just the shift in features, but also the change in their shape. Modeling a shape change as well as a shift results in greater accuracy. This method, ICGN-based HREBSD, is applied to a simulated data set, and its performance is compared to conventional cross-correlation HREBSD, and cross-correlation HREBSD with remapping. ICGN-based HREBSD is shown to have about half the strain error of the best cross-correlation method with a comparable computation time.

Local Strain Distribution and Microstructure of Grinding-Induced Damage Layers in SiC Wafer

The high-angular-resolution electron backscatter diffraction (HR-EBSD) technique has been utilized to evaluate the elastic strain distribution of grinding-induced damage layers in silicon carbide wafers. HR-EBSD analysis, along with transmission electron microscopy observation, revealed that the damage layers formed beneath the wafer surface when the surface was ground by diamond abrasives; the layers were classified hierarchically based on the distribution of elastic strain and lattice defects. In particular, very large elastic strain formed in a defective region of roughly 0.6 μm in thickness, just beneath the ground wafer surface, where lattice defects such as dislocations, stacking faults, and microcracks were introduced inhomogeneously by abrasive interaction and related plastic deformation and fracture. Based on this inhomogeneity, the defective region was itself classified into two types: one, a highly defective region with very large, complicated strain and high defect density; and the other, a basal plane dislocation (BPD)-glide region, with small strain and few BPDs or stacking faults. Beneath the defective region, a strain gradient region of roughly 1.8 μm in thickness, which was unambiguously identified by HR-EBSD strain analysis alone, revealed a monotonic gradient in the dominant compressive strain component, with no grinding-induced defects. Overall, HR-EBSD analysis revealed a nanometer-scale, hierarchical elastic strain distribution in the grinding-induced damage layers.

Grain Boundary Serration in Nickel-Based Superalloy Inconel 600: Generation and Effects on Mechanical Behavior

Grain boundary serration in the superalloy Inconel 600 was studied. Two microstructural variants, one with nonserrated and the other with serrated grain boundaries were generated by altering the heat-treatment conditions, while keeping other aspects of the microstructure unchanged. The effect on the creep response between 700 °C and 900 °C was measured, and the different failure modes and accumulated damage were quantified using high-angular resolution electron backscatter diffraction analysis in the scanning electron microscope and also by X-ray computed tomography. It is found that serration plays a more crucial role in the high-temperature/low-stress regime when an intergranular cracking mechanism involving cavitation is operative; here it plays a role in improving both creep life and creep ductility. Any effect of serration is less prevalent at low temperatures where transgranular failure is dominant.

A consistent full-field integrated DIC framework for HR-EBSD

A general, transparent, finite-strain Integrated Digital Image Correlation (IDIC) framework for high angular resolution EBSD (HR-EBSD) is proposed, and implemented through a rigorous derivation of the optimization scheme starting from the fundamental brightness conservation equation in combination with a clear geometric model of the Electron BackScatter Pattern (EBSP) formation. This results in a direct one-step correlation of the full field-of-view of EBSPs, which is validated here on dynamically simulated patterns. Strain and rotation component errors are, on average, (well) below 10−5 for small (Eeq=0.05%) and medium (Eeq=0.2%) strain, and below 3×10−5 for large strain (Eeq=1%), all for large rotations up to 10° and 2% image noise. High robustness against poor initial guesses (1° misorientation and zero strain) and typical convergence in 5 iterations is consistently observed for, respectively, image noise up to 20% and 5%. This high accuracy and robustness rivals, when comparing validation on dynamically simulated patterns, the most accurate HR-EBSD algorithms currently available which combine sophisticated filtering and remapping strategies with an indirect two-step correlation approach of local subset ROIs. The proposed general IDIC/HR-EBSD framework lays the foundation for future extensions towards more accurate EBSP formation models or even absolute HR-EBSD.

Understanding deformation with high angular resolution electron backscatter diffraction (HR-EBSD)

High angular resolution electron backscatter diffraction (HR-EBSD) affords an increase in angular resolution, as compared to ‘conventional’ Hough transform based EBSD, of two orders of magnitude, enabling measurements of relative misorientations of 1 x 10−4 rads (~ 0.006°) and changes in (deviatoric) lattice strain with a precision of 1 x 10−4. This is achieved through direct comparison of two or more diffraction patterns using sophisticated cross-correlation based image analysis routines. Image shifts between zone axes in the two-correlated diffraction pattern are measured with sub-pixel precision and this realises the ability to measure changes in interplanar angles and lattice orientation with a high degree of sensitivity. These shifts are linked to strains and lattice rotations through simple geometry. In this manuscript, we outline the basis of the technique and two case studies that highlight its potential to tackle real materials science challenges, such as deformation patterning in polycrystalline alloys.

Quantifying geometrically necessary dislocations in quartz using HR-EBSD: Application to chessboard subgrain boundaries

This study presents the first use of high-angular resolution electron backscatter diffraction (HR-EBSD) to quantitatively characterise geometrically necessary dislocations in quartz subgrain structures. HR-EBSD exploits cross-correlation of diffraction patterns to measure intragranular misorientations with precision on the order of 0.01° with well-constrained misorientation axes. We investigate the dislocation structures of chessboard subgrains in quartz within samples from the Greater Himalayan Sequence, Nepal. Our results demonstrate that chessboard subgrains are formed primarily from two sets of subgrain boundaries. One set consists primarily of {m}[c] edge dislocations, the other consists primarily of dislocations with <a> Burgers vectors. Apparent densities of geometrically necessary dislocations vary from > 1013 m−2 within some subgrain boundaries to < 1012 m−2 within subgrain interiors. The results suggest that at pressures above approximately 10 kbar, chessboard subgrains may form within the α-quartz stability field. Most importantly, this study demonstrates the potential of HR-EBSD as an improved method for analysis of intragranular microstructures in quartz that are used as indicators of deformation conditions.

Preventing damage and redeposition during focused ion beam milling: The “umbrella” method

Focused ion beam (FIB) milling has enabled the development of key microstructure characterization techniques (e.g. 3D electron backscatter diffraction (EBSD), 3D scanning electron microscopy imaging, site-specific sample preparation for transmission electron microscopy, site-specific atom probe tomography), and micro-mechanical testing techniques (e.g. micro-pillar compression, micro-beam bending, in-situ TEM nanoindentation). Yet, in most milling conditions, some degree of FIB damage is introduced via material redeposition, Ga+ ion implantation or another mechanism. The level of damage and its influence vary strongly with milling conditions and materials characteristics, and cannot always be minimized. Here, a masking technique is introduced, that employs standard FIB-SEM equipment to protect specific surfaces from redeposition and ion implantation. To investigate the efficiency of this technique, high angular resolution EBSD (HR-EBSD) has been used to monitor the quality of the top surface of several micro-pillars, as they were created by milling a ringcore hole in a stress-free silicon wafer, with or without protection due to an “umbrella”. HR-EBSD provides a high-sensitivity estimation of the amount of FIB damage on the surface. Without the umbrella, EBSD patterns are severely influenced, especially within 5 µm of the milled region. With an optimized umbrella, sharp diffraction patterns are obtained near the hole, as revealed by average cross correlation factors greater than 0.9 and equivalent phantom strains of the order 2 × 10−4. Thus, the umbrella method is an efficient and versatile tool to support a variety of FIB based techniques.

Selectively Electron-Transparent Microstamping Toward Concurrent Digital Image Correlation and High-Angular Resolution Electron Backscatter Diffraction (EBSD) Analysis.

Digital image correlation (DIC) in a scanning electron microscope and high-angular resolution electron backscatter diffraction (HREBSD) provide valuable and complementary data concerning local deformation at the microscale. However, standard surface preparation techniques are mutually exclusive, which makes combining these techniques in situ impossible. This paper introduces a new method of applying surface patterning for DIC, namely a urethane microstamp, that provides a pattern with enough contrast for DIC at low accelerating voltages, but is virtually transparent at the higher voltages necessary for HREBSD and conventional EBSD analysis. Furthermore, microstamping is inexpensive and repeatable, and is more suitable to the analysis of patterns from complex surface geometries and larger surface areas than other patterning techniques.

Growth of {[formula omitted]} twins in titanium: A combined experimental and modelling investigation of the local state of deformation

In this work we combine experiments and simulations to study the residual deformation state near twins in titanium at different stages of the complete twin growth process, including the twin tip: (i) far from a grain boundary, (ii) approaching a grain boundary, and (iii) intersecting with a grain boundary. High resolution electron backscatter diffraction (HR-EBSD) was used to characterise the local residual stress state and dislocation density distributions. Schmid factors were calculated from both the global deformation state (i.e. remote loading) and local deformation state (i.e. from high angular resolution EBSD). Crystal plasticity finite element modelling was used to simulate the stress field close to twins during loading and unloading. These simulations indicate that while the magnitudes of the localized stress fields close to twin boundaries are reduced upon removing the far field load, the major features of the stress fields in these regions are dominated by accommodation of the twin and thus persist from the peak load state to the unloaded state. We find a good correlation between the active twin variant and the maximum local Schmid factor, while the external loading (i.e. global Schmid factor) plays a less important role. These findings are useful in determining which twins will grow when a sample is deformed, and this has important implications for in service performance as well as texture evolution during mechanical processing.

An Experimental Study on Evolution of Grain‐Scale Stress/Strain and Geometrical Necessary Dislocations in Advanced TA15 Titanium Alloy during Uniaxial Tension Deformation

This study aims to characterize the spatial distributions of grain‐scale stress/strain and geometrical necessary dislocations (GNDs) in TA15 titanium alloy subjected to tensile deformation at room temperature. The microstructures under different strains are investigated through electron backscatter diffraction (EBSD) measurements. Evolution of intergranular stress/strain is revealed by analysis of high angular resolution EBSD patterns. The spatial distributions of GNDs are calculated using a self‐developed routine. Results indicate that many factors influence the spatial distributions of grain‐scale residual stress/strain and GNDs during plastic deformation, and the dominant factor varies with the changes in microstructure characteristics and macroscopic deformation parameters.

On the nucleation and growth of {[formula omitted]} twin in commercial purity titanium: In situ investigation of the local stress field and dislocation density distribution

Compression testing was conducted on a micro-pillar consisting of a soft-hard grain pair. A {112¯2}<112¯3¯> contraction twin variant nucleated at the edge of the hard grain and elongated progressively into the pillar towards the grain boundary. High angular resolution EBSD scans were performed in situ during the compression testing in order to characterize the elastic strain field and dislocation density distribution at the twin-parent interface during the twin growth. The local/global shear stress ratio on the active twin variant increased from ∼1.6, before macroscopic yielding, to ∼4.2 at peak load, and the rate of increase is inversely proportional to the macroscopic strain level. While the active twin variant does not have the highest global shear stress, it does experience a higher local shear compared to other twin variants, which may contribute to its nucleation. The elongation of the active twin variant involves a competition between local shear stress and dislocation density in front of the twin tip. This could lead to a discontinuous elongation process and stop twin from reaching grain boundary—a phenomenon frequently observed from large grain materials. After removal of the external loading, twinning shear partially reversed sign along the twin-parent interface, indicating a tendency to de-twin.

Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction

Dislocations in geological minerals are fundamental to the creep processes that control large-scale geodynamic phenomena. However, techniques to quantify their densities, distributions, and types over critical subgrain to polycrystal length scales are limited. The recent advent of high-angular resolution electron backscatter diffraction (HR-EBSD), based on diffraction pattern cross-correlation, offers a powerful new approach that has been utilised to analyse dislocation densities in the materials sciences. In particular, HR-EBSD yields significantly better angular resolution (<0.01°) than conventional EBSD (~0.5°), allowing very low dislocation densities to be analysed. We develop the application of HR-EBSD to olivine, the dominant mineral in Earth's upper mantle by testing (1) different inversion methods for estimating geometrically necessary dislocation (GND) densities, (2) the sensitivity of the method under a range of data acquisition settings, and (3) the ability of the technique to resolve a variety of olivine dislocation structures. The relatively low crystal symmetry (orthorhombic) and few slip systems in olivine result in well constrained GND density estimates. The GND density noise floor is inversely proportional to map step size, such that datasets can be optimised for analysing either short wavelength, high density structures (e.g. subgrain boundaries) or long wavelength, low amplitude orientation gradients. Comparison to conventional images of decorated dislocations demonstrates that HR-EBSD can characterise the dislocation distribution and reveal additional structure not captured by the decoration technique. HR-EBSD therefore provides a highly effective method for analysing dislocations in olivine and determining their role in accommodating macroscopic deformation.

Crack nucleation using combined crystal plasticity modelling, high-resolution digital image correlation and high-resolution electron backscatter diffraction in a superalloy containing non-metallic inclusions under fatigue.

A crystal plasticity finite-element model, which explicitly and directly represents the complex microstructures of a non-metallic agglomerate inclusion within polycrystal nickel alloy, has been developed to study the mechanistic basis of fatigue crack nucleation. The methodology is to use the crystal plasticity model in conjunction with direct measurement at the microscale using high (angular) resolution-electron backscatter diffraction (HR-EBSD) and high (spatial) resolution-digital image correlation (HR-DIC) strain measurement techniques. Experimentally, this sample has been subjected to heat treatment leading to the establishment of residual (elastic) strains local to the agglomerate and subsequently loaded under conditions of low cyclic fatigue. The full thermal and mechanical loading history was reproduced within the model. HR-EBSD and HR-DIC elastic and total strain measurements demonstrate qualitative and quantitative agreement with crystal plasticity results. Crack nucleation by interfacial decohesion at the nickel matrix/agglomerate inclusion boundaries is observed experimentally, and systematic modelling studies enable the mechanistic basis of the nucleation to be established. A number of fatigue crack nucleation indicators are also assessed against the experimental results. Decohesion was found to be driven by interface tensile normal stress alone, and the interfacial strength was determined to be in the range of 1270–1480 MPa.

On the origin of creep dislocations in a Ni-base, single-crystal superalloy: an ECCI, EBSD, and dislocation dynamics-based study

This work investigates the origin of creep dislocations in a Ni-base, single crystal superalloy subject to creep at an intermediate stress and temperature. Employing high angular resolution electron backscatter diffraction (HR-EBSD), electron channeling contrast imaging under controlled diffraction conditions (cECCI) and discrete dislocation dynamics (DDD) modelling, it is shown that low-angle boundaries—which correspond to dendrite boundaries or their residues after annealing—are not the major sources of creep dislocations. At the onset of creep deformation, they are the only active sources. Creep dislocations are emitted from them and percolate into the dislocation-depleted crystal. However, the percolation is very slow. As creep deformation proceeds, before the boundary-originated dislocations move further than a few micrometers away from their source boundary, individual dislocations that are spread throughout the undeformed microstructure become active and emit avalanches of creep dislocations in boundary-free regions, i.e. regions farther than a few micrometer away from boundaries. Upon their activation, the density of creep dislocations in boundary-free regions soars by two orders of magnitude; and the entire microstructure becomes deluged with creep dislocations. ​The total area of boundary-free regions is several times the total area of regions covered by boundary-originated creep dislocations. Therefore, the main sources of creep dislocations are not low-angle boundaries but individual, isolated dislocations in boundary-free regions.

Deformation compatibility in a single crystalline Ni superalloy.

Deformation in materials is often complex and requires rigorous understanding to predict engineering component lifetime. Experimental understanding of deformation requires utilization of advanced characterization techniques, such as high spatial resolution digital image correlation (HR-DIC) and high angular resolution electron backscatter diffraction (HR-EBSD), combined with clear interpretation of their results to understand how a material has deformed. In this study, we use HR-DIC and HR-EBSD to explore the mechanical behaviour of a single-crystal nickel alloy and to highlight opportunities to understand the complete deformations state in materials. Coupling of HR-DIC and HR-EBSD enables us to precisely focus on the extent which we can access the deformation gradient, F, in its entirety and uncouple contributions from elastic deformation gradients, slip and rigid body rotations. Our results show a clear demonstration of the capabilities of these techniques, found within our experimental toolbox, to underpin fundamental mechanistic studies of deformation in polycrystalline materials and the role of microstructure.

Slip localization and fatigue crack nucleation near a non-metallic inclusion in polycrystalline nickel-based superalloy

Fatigue crack nucleation at a non-metallic agglomerate inclusion has been studied by high spatial resolution Digital Image Correlation (HR-DIC) and high angular resolution Electron Backscatter Diffraction (HR-EBSD). Spatial and temporal characterization and correlation of deformation with underlying microstructures has been performed, with distributions of plastic strain measured from HR-DIC; and residual stress and density of geometrically necessary dislocations (GND) measured from HR-EBSD. Initial residual stress and GND fields, as a consequence of differing thermal expansivities in the metallic and oxide phases, localized around the agglomerate have been quantified using HR-EBSD. The localization of the pre-existing stress and dislocation states appear to lead to early onset of plasticity upon subsequent mechanical loading. Heterogeneous distributions of plastic strain have been observed in the course of the fatigue test by HR-DIC. Crack nucleation via agglomerate/nickel interface decohesion and particle fracture has been demonstrated and this is correlated with the elevation in strain and dislocation density. The measurements of residual stress, strain, and dislocation density provide key information for the mechanisms of fatigue cracking and the development of damage nucleation criteria in these material systems.

Measurements of stress fields near a grain boundary: Exploring blocked arrays of dislocations in 3D

The interaction between dislocation pile-ups and grain boundaries gives rise to heterogeneous stress distributions when a structural metal is subjected to mechanical loading. Such stress heterogeneity leads to preferential sites for damage nucleation and therefore is intrinsically linked to the strength and ductility of polycrystalline metals. To date the majority of conclusions have been drawn from 2D experimental investigations at the sample surface, allowing only incomplete observations. Our purpose here is to significantly advance the understanding of such problems by providing quantitative measurements of the effects of dislocation pile up and grain boundary interactions in 3D. This is accomplished through the application of differential aperture X-ray Laue micro-diffraction (DAXM) and high angular resolution electron backscatter diffraction (HR-EBSD) techniques. Our analysis demonstrates a similar strain characterization capability between DAXM and HR-EBSD and the variation of stress intensity in 3D reveals that different parts of the same grain boundary may have different strengths in resisting slip transfer, likely due to the local grain boundary curvature.

On solving the orientation gradient dependency of high angular resolution EBSD

Current high angular resolution electron backscatter diffraction (HR-EBSD) methods are successful at measuring pure elastic strains but have difficulties with plastically deformed metals containing orientation gradients. The strong influences of these rotations have been systematically studied using simulated patterns based on the many-beam dynamic theory of EBSP formation; a rotation of only 1 can lead to apparent elastic strains of several hundred microstrains. A new method is proposed to correct for orientation gradient effects using a two-step procedure integrating finite strain theory: (i) reference pattern rotation and (ii) cross-correlation; it reduces the strain errors on the simulated patterns to tens of microstrains. An application to plastically deformed ferritic steel to generates elastic strain maps with significantly reduced values of both strains and residual errors in regions of rotations exceeding 1 degrees.

The effect of crystal orientation on the indentation response of commercially pure titanium: experiments and simulations

This study combines nanoindentation, electron backscatter diffraction (EBSD) and crystal plasticity finite element analysis to examine the anisotropy in the indentation behaviour of individual grains within an α-Ti polycrystal. Nanoindentation is utilized to mechanically probe small volumes of material within grains for which orientations are known from prior EBSD mapping. Both indentation modulus and hardness decrease significantly as the indentation axis is inclined further from the c -axis; the plastic response showing the more marked anisotropy. Recently developed high angular resolution EBSD has been utilized to examine selected indents, providing maps of elastic strain variations and lattice rotations. From such maps lower bound solutions for the density of geometrically necessary dislocations (GNDs) have been established. Crystal plasticity modelling showed promise in capturing correctly the orientation dependence of load–displacement response and in lattice rotations local to the indenter, particularly for indentation into a basal plane which generated threefold rotational symmetry about an axis parallel with the indentation direction which was also observed in experiments.